Whirlybird


Yr 11 MATHS B


ASSIGNMENT


Task one


The aim of this assignment was to determine and create the most suitable and efficient Whirlybird which could sustain flight times the longest. The method followed to achieve this was a series of flight test. Different sizes of Whirly birds were created in 2cm intervals in the length and the width. Then each model will be dropped from the same height keeping all variables the same, six times and recording the flight time to the ground. The recorded flight times will be analysed and used to determine the best Whirlybird. It will be analysed using different mathematical methods and graphs to provide suggestions. The process taken to complete the experiment followed the method explicitly. The recording of the whirlybird drops were unaffected by natural elements such as the weather because it was kept indoor in a controlled environment (wind resistance and hight control were not a problem). The timing using a stop watch was kept by the same person so reaction time would not defer while recording. When transferring the data to a computer for analysis, the means and standard deviation were calculated for each of the six drops of each whirlybird and put into datal plots. The data plots were used to break down the information and put into TI Interactive. It would then use it aid in the analysis process by plotting graphs and calculating a regression.


Task 2


Lengths cm


1ts


2nd


3rd


4th


5th


6th


mean


SD


2


1.42


1.78


2.03


2.08


1.6


1.42


1.7217


0.291


4


2.82


1.87


3.07


3.16


2.55


2.86


2.7217


0.4684


6


3.72


3.6


3.51


4.37


4.05


3.69


3.8234


0.3246


8


4.3


4.96


6.01


4.64


4.93


4.95


4.756


0.2876


10


5.56


5.38


4.66


4.89


4.82


4.77


5.0134


0.36604


12


3.76


3.87


3.57


4.03


3.02


3.74


3.655


0.3506


14


1.92


1.89


2.3


2.48


3.42


3.25


2.8625


0.5548


16


2.01


2.32


2.35


1.81


1.98


2.12


2.0984


0.2088


The data above is all the information gathered during the wing length flight tests, it was used during the experiment for the analysis process. It consists of the six drops for each whirly bird and the mean and standard deviation of each set. The Mean and standard deviation were calculated to easily identify the best length for a whirlybird. The data marked in RED were selected as the out riders they were taken out of the calculation to ensure the results were ordinary and not unique for the information.


Task 3


The data below is the graphical representation of the results recorded during the flight test for the best length of a whirly bird. TI Interactive was used because of it ability to produced the most accurate and reliable results for finding the quadratic regression and line of best fit for the graph. The graph bellow was chosen because it depicts the movements of the data accurately along the graph.



(9.16379, 4.55496) Maximum


Task 4


A separate investigation was set up to the determine the best width for the whirlybirds wings. It followed the same process and method as the first experiment. Except for the fact that the width length would only be between one and three cm. It had the same six drops for each of the three whirlybirds and was recorded under the same conditions as the first experiment, it was then recorded and the same calculations were made before transferring the data onto a computer. It was then analysed and the following were created using TI Interactive quadratic regression, a graphical display and data table.


Task 5


Width cm


1st


2nd


3rd


4th


5th


6th


mean


SD


1


2.01


2.32


2.35


1.81


1.98


2.12


2.0983


0.2088


2


1.8


2.19


2.08


2.28


1.89


2.11


2.048


0.2009


3


2.7


5.22


5.76


4.68


2.7


7.09


4.6917


1.7381


The data above is all the information gathered during the wing Width flight tests; it was used during the experiment for the analysis process. It consists of the six drops for each whirly bird and the mean and standard deviation of each set. The Mean and standard deviation were calculated to easily identify the best Width for a whirlybird. The data marked in RED were selected as the out riders they were taken out of the calculation to ensure the results were ordinary and not unique for the information.


Task 6


The data below is the graphical representation of the results recorded during the flight test for the best width of a whirly bird. TI Interactive was used because of it ability to produced the most accurate and reliable results for finding the quadratic regression and line of best fit for the graph. The graph bellow was chosen because it depicts the movements of the data accurately along the graph.


Task 7


TI Interactive and Microsoft Excel were used as my software of choice in my graphical and mathematical representation of, my data in tasks three and six. Excel was used during the experiment for table representation of the data recorded and easily